Looking at teacher prep programs or candidates’ personal characteristics doesn’t help, the No Guarantees report found. Post-training tests don’t show where to set the bar either.

“Teachers who perform better on the Praxis math are, on average,
better math teachers,” Aldeman writes. “But the differences are tiny,
and there is wide variation at nearly every score"...

Without reliable screening tools, states should eliminate “unhelpful
barriers” to entering the teaching profession and “let districts take
responsibility for training and evaluating their employees,” he
concludes.

I see very good potential benefits from such a proposal, as well as very deep potential pitfalls. At least we know what we're getting with today's system; would it be right to conduct the above experiment on other people's children?